Algebra and Number Theory
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German
This lecture continues the linear algebra courses. It treats groups, rings, fields and applications in the number theory and geometry. The highlights of the lecture are the classification of finite fields, the impossibility of the trisection of angles with circle and ruler, the non-existence of a solution formula for the general equations of fifth degree and the quadratic reciprocity law.
Required: Linear Algebra~I and II
Algebra and Number Theory (2HfB21, MEH21)
Compulsory Elective in Mathematics (BSc21)
Introduction to Algebra and Number Theory (MEB21)
Algebra and Number Theory (MEdual24)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar
Seminar: Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Wolfgang Soergel
Assistant: Xier Ren
Language: in German
In linear algebra you studied linear systems of equations. In commutative algebra, we study polynomial equation systems such as \(x^2+y^2 = \) 1 and their solution sets, the algebraic varieties. It will turn out that such a variety is closely related to the ring of the restrictions of polynomial functions on that variety, and that we can extrapolate this relationship to a geometric understanding of any commutative rings, in particular the ring of the integers. Commutative algebra, algebraic geometry, and number theory grow together in this conceptual building. The lecture aims to introduce into this conceptual world. We will especially focus on the dimension of algebraic varieties and their cutting behavior, which generalizes the phenomena known from the linear algebra on the case of polynomial equation systems.
necessary: Linear Algebra I+II
useful: Algebra and Number Theory
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Do, 10-12h, SR 403, Ernst-Zermelo-Str. 1
Preregistration: by e-mail to Wolfgang Soergel
Preliminary Meeting 28.01., 14:15, SR 127, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: Talk/participation possible in German and English
This seminar is intended to introduce to the theory of linear algebraic groups. Linear algebraic groups are generalizations of the matrix groups known from linear algebra.
I imagine a format in which I or Sercombe lecture and in between the seminar participants give talks. The seminar is a reasonable addition to the commutative algebra lecture. Reference to that lecture increase in the course of the seminar.
Algebra and Number Theory (where the details of Galois theory and field theory are less relevant than the general theory of groups and rings) and Linear Algebra.
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
25.02., 13:00-16:00, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 09.04., 09:00-12:00
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German
This lecture continues the linear algebra courses. It treats groups, rings, fields and applications in the number theory and geometry. The highlights of the lecture are the classification of finite fields, the impossibility of the trisection of angles with circle and ruler, the non-existence of a solution formula for the general equations of fifth degree and the quadratic reciprocity law.
Required: Linear Algebra~I and II
Algebra and Number Theory (2HfB21, MEH21)
Compulsory Elective in Mathematics (BSc21)
Introduction to Algebra and Number Theory (MEB21)
Algebra and Number Theory (MEdual24)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)
Mathematical Physics
Lecture: Di, 16-18h, SR 403, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Language: in German
Introduction to classic mechanics from the point of view of mathematics. We start with the mathematical modelling of space and time. Then we discuss Newton's equations of movement, physical systems with compulsory conditions, the D'Alembert principle, the Hamilton formalism and its derivation from the Newton's equations and applications of Hamilton formalism.
Required: Analysis III
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)
Seminar: Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preregistration:
Preparation meetings for talks: Dates by arrangement
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German
In this proseminar we will discuss topics that are found in various textbooks and scripts for basic lectures in linear algebra but which are not part of the standard material. The lectures build on each other only slightly.
Linear Algebra ~I and II, Analysis~I and II.
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
07.03., 09:00-12:00
Teacher: Wolfgang Soergel
Assistant: Giovanni Zaccanelli
general:
Analysis III (BSc21)
Mathematical Concentration (MEd18, MEH21)
Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Vivien Vogelmann
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Lecture: Mo, Mi, 8-10h, HS Rundbau, Albertstr. 21
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general: ,
Analysis II (BScInfo19, BScPhys20)
Seminar: Lie-Algebren
Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Vivien Vogelmann
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Lecture: Mi, Di, 8-10h, HS Rundbau, Albertstr. 21
28.03., 09:00-12:00
Sit-in exam (resit) 12.09., 09:00-12:00
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general: ,
Di, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Topologie
Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b
27.07., 10:00-12:00
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general:
Pure Mathematics (MSc14)
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Proseminar: Gemischte Kost
Mo, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Seminar des Graduiertenkollegs 1821
Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Assistant: Vivien Vogelmann
Funktionentheorie
Teacher: Wolfgang Soergel
Assistant: Johan Commelin
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, bbb-Raum "Anderssen", online
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Seminar des Graduiertenkollegs 1821
Mi Do, 14-16h, bbb-Raum des Graduiertenkollegs, online
Teacher: Andriy Haydys, Annette Huber-Klawitter, Fritz Hörmann, Stefan Kebekus, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland
Assistant: Jonas Schnitzer
Algebraische Gruppen
Lecture: Mi, Mo, 10-12h, , online
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Seminar des Graduiertenkollegs 1821
Mi 14-16h, SR 125, Ernst-Zermelo-Str. 1, Do, 14-16h, bbb-Raum "Krush", online
Teacher: Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Wolfgang Soergel, Stefan Kebekus, Katrin Wendland
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, , online
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Mathematisch-Physikalisches Kolloquium
Fr, 14-17h, wechselnder Hörsaal, -
Teacher: Andreas Buchleitner, Nadine Große, Wolfgang Soergel, Katrin Wendland
Kommutative Algebra und Einführung in die algebraische Geometrie
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Teacher: Wolfgang Soergel
Assistant: Giovanni Zaccanelli
general:
Compulsory Elective in Mathematics (BSc21)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Stefan Kebekus, Wolfgang Soergel
Seminar des Graduiertenkollegs 1821
Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Andriy Haydys, Stefan Kebekus, Wolfgang Soergel, Katrin Wendland
Mathematisch-Physikalisches Kolloquium
Fr, 14-17h, wechselnder Hörsaal, -
Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland
Algebra und Zahlentheorie
Lecture: Do, Di, 10-12h, HS Weismann-Haus, Albertstr. 21a
03.03., 09:00-12:00
Sit-in exam (resit) 05.05., 09:00-13:00
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general: ,
Algebra and Number Theory (2HfB21, MEH21)
Pure Mathematics (MSc14)
Compulsory Elective in Mathematics (BSc21)
Seminar des Graduiertenkollegs 1821
Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Wolfgang Soergel, Katrin Wendland, Stefan Kebekus
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Mathematisch-Physikalisches Kolloquium
Fr, 14-17h, wechselnder Hörsaal, -
Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland
Nichtkommutative Algebra und Symmetrie
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
25.07., 08:00-10:00
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Wolfgang Soergel
Seminar des Graduiertenkollegs 1821
Mi 14-16h, SR 404, Ernst-Zermelo-Str. 1, Di, 12-14h, SR 218, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Andriy Haydys, Wolfgang Soergel, Katrin Wendland
Mathematisch-Physikalisches Kolloquium
Fr, 14-17h, wechselnder Hörsaal, -
Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland
Lie-Algebren und ihre Darstellungen
Teacher: Wolfgang Soergel
general:
Seminar: Spiegelungsgruppen
Di, 8-10h, HS II, Albertstr. 23b
Teacher: Wolfgang Soergel
Assistant: Leonardo Patimo
general:
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Oberseminar: Algebra, Zahlentheorie und algebraische Geometrie
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Seminar des Graduiertenkollegs 1821
Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel, Katrin Wendland, Andriy Haydys, Fritz Hörmann
Mathematisch-Physikalisches Kolloquium
Fr, 14-17h, wechselnder Hörsaal, -
Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Emmanuel Scheidegger, Wolfgang Soergel, Katrin Wendland